Exponential Integral Calculator

Published on: July 17, 2026
Final Answer: Free • Full Steps: Plus

This Exponential Integral Calculator helps you integrate exponential functions such as e^x, 2e^x, or 3^x. The natural exponential e^x is its own antiderivative, while a general base a^x picks up a factor of 1/ln(a).

Step-by-step method

  1. Identify the exponential function and any constant multiple.
  2. Write the integration rule for that exponential function.
  3. Apply the rule, keeping the constant multiple in front, and add C.

Formula:

\(\begin{gathered} \int e^{x}\, dx = e^{x} + C \\ \int a^{x}\, dx = \frac{a^{x}}{\ln\left(a\right)} + C \end{gathered}\)

Example 1:

\(\int e^{x}\, dx\)

Step 1 - Identify the exponential function and any constant multiple.

In this problem: The function is \(e^{x}\).

\(\int e^{x}\, dx\)

Step 2 - Write the integration rule for that exponential function.

In this problem: The integral of \(e^{x}\) is itself.

\(\int e^{x}\, dx = e^{x} + C\)

Step 3 - Apply the rule, keeping the constant multiple in front, and add C.

In this problem: The antiderivative is \(e^{x}\).

\(\int e^{x}\, dx = e^{x} + C\)

Final answer:

\(\int e^{x}\, dx = e^{x} + C\)

Example 2:

\(\int 3^{x}\, dx\)

Step 1 - Identify the exponential function and any constant multiple.

In this problem: The function is \(3^{x}\).

\(\int 3^{x}\, dx\)

Step 2 - Write the integration rule for that exponential function.

In this problem: The integral of \(3^{x}\) is the function divided by the natural logarithm of the base \(3\).

\(\int a^{x}\, dx = \frac{a^{x}}{\ln\left(a\right)} + C\)

Step 3 - Apply the rule, keeping the constant multiple in front, and add C.

In this problem: The antiderivative is \(\frac{3^{x}}{\ln\left(3\right)}\).

\(\int 3^{x}\, dx = \frac{3^{x}}{\ln\left(3\right)} + C\)

Final answer:

\(\int 3^{x}\, dx = \frac{3^{x}}{\ln\left(3\right)} + C\)